7-5y=4y^2

Solution for 7-5y=4y^2 equation:

7-5y=4y^2

We move all terms to the left:

7-5y-(4y^2)=0

determiningTheFunctionDomain
-4y^2-5y+7=0

a = -4; b = -5; c = +7;
Δ = b2-4ac
Δ = -52-4·(-4)·7
Δ = 137
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{137}}{2*-4}=\frac{5-\sqrt{137}}{-8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{137}}{2*-4}=\frac{5+\sqrt{137}}{-8}
$